Before they had been interrupted by her family (again) Kara Danvers and James Olsen had been quite content. The gifting of the photo had helped ease a few of Kara's concerns when it came to their relationship. To Kara it showed that James was not only attracted to her because he knew she was Supergirl but was also attracted to plain old Kara Danvers, who occasionally had trouble stringing together a sentence.
For James Olsen, the photo was to show that even with all the constant interruptions they hadn't missed their 'moment'.